Two Court of Appeal judges said the attack, which was filmed by a bystander on a mobile phone, was "brutal".

Daniel Mogoai and James Alexander, both aged 23, were jailed for two years and six months with a non-parole period of one year after pleading guilty to recklessly causing serious injury and affray.

Both men appealed their sentences, claiming they were manifestly excessive, but Court of Appeal Justices Robert Redlich and Phillip Priest rejected the appeal on Monday.

The appeal judges said the two men, along with Mogoai's younger brother, Blake, and two young women, Rhiannon Hocking and Almaz Rios, were involved in an attack on Djordje Dimitrijevic and Darko Jakovijevic in the early hours of April 25, 2012, on Chapel Street, South Yarra.

Mr Jakovijevic, who had been drinking nearby with friends, had gone into a convenience store to buy cigarettes and a bottle of water when he argued with Ms Hocking and told her to hurry up.

Mr Jakovijevic then walked to his friend's car where Mr Dimitrijevic was waiting.

Ms Hocking and Ms Rios began shouting abuse at both Mr Jakovijevic and Mr Dimitrijevic.

When the two men spoke Serbian, Ms Rios took offence and said, "In Australia, we need to speak English".

Ms Hocking called Alexander who arrived a short time later with Mogoai.

"The court viewed a video of the attack, which had been recorded by a bystander on a mobile telephone," the appeal judges said.

"The video graphically depicts the assault, which the sentencing judge, correctly, in our view, found to be unprovoked.

"Plainly, the situation that confronted the victims was made extremely volatile by the shameful actions of the two females, who encouraged the appellants and Blake Mogoai to attack the victims.

"The physical violence is seen to commence when Blake Mogoai begins throwing punches at Mr Jakovijevic, whom he then pursues around the back of the car as Mr Jakovijevic tries to escape. Shortly afterward, Mr Dimitrijevic is seen to be attacked by the appellants.

"Mr Dimitrijevic is shown to be backed against the parked car, when he suffers a savage volley of punches from the appellants.

"He can be seen to be doing little to defend himself from the brutal attack being mounted, ineffectually waving his arms around and unable to escape the raining blows.

"It was, to say the very least, a nasty assault, and the video is sickening to watch.

"A particularly unpleasant aspect is the final vicious punch delivered by the appellant Mogoai. The sound of the blow connecting with Mr Dimitrijevic's face is nothing short of nauseating."

The judges said while the court "must be careful not to succumb to an emotional response to the violence perpetrated, and must approach the circumstances of the offence [and those of the offenders] in a balanced and objective manner, nonetheless the video footage helps one to gauge the gravity of the offending".

Mr Dimitrijevic suffered multiple fractures around his eyes and nose requiring hospitalisation, surgery and the insertion of metal plates around his eye sockets.